Erlang Strength Model for Exponential Effects

All technical systems have been designed to performtheir intended tasks in a specific ambient. Some systemscan perform their tasks in a variety of distinctive levels.A system that can have a finite number of performancerates is called a multi-state system. Generally multi-statesystem is consisted of components that they also can bemulti-state. The performance rates of components constitutinga system can also vary as a result of their deteriorationor in consequence of variable environmental conditions.Components failures can lead to the degradationof the entire multi-state system performance. The performancerates of the components can range from perfectfunctioning up to complete failure. The quality of the systemis completely determined by components. In this article,a possible state for the single component system,where component is subject to two stresses, is consideredunder stress-strength model which makes the componentmulti-state. The probabilities of component are studiedwhen strength of the component is Erlang random variablesand the stresses are independent exponential randomvariables. Also, the probabilities of component areconsidered when the stresses are dependent exponentialrandom variables.